Water-soluble polymers possess great advantages in current drug delivery systems, such as fast delivery through polymer matrix dissolution as well as promoting solid dispersion of poorly water-soluble drugs. In this work, water-soluble polyvinyl alcohol (PVA) and polyethylene oxide (PEO) were blended (50/50) to electrospin with and without the incorporation of a model drug, melatonin (MLT), at various blend polymer concentrations. Results suggested that increasing blend PVA/PEO solution concentrations, up to 7 wt%, promoted the formation of smooth and defect-free drug-incorporating fibers with an average fiber diameter ranged from 300 to 700 nm. Mechanical properties of the blank and MLT-loaded PVA/PEO fibers showed dependence on fiber morphologies and fiber mat structures, due to polymer concentrations for electrospinning. Furthermore, the surface wettability of the blend PVA/PEO fibers were investigated and further correlated with the MLT release profile of the fibers. Results suggested that fiber mats with a more well-defined fiber structure promoted a linear release behavior within 10 minutes in vitro. These drug-incorporated fibers were compatible to human umbilical vein endothelial cells (HUVECs) up to 24 hours. In general, this work demonstrated the structure-property correlations of electrospun PVA/PEO fibers and their potential biomedical applications in fast delivery of small molecule drugs.
Citation: Rachel Emerine, Shih-Feng Chou. Fast delivery of melatonin from electrospun blend polyvinyl alcohol and polyethylene oxide (PVA/PEO) fibers[J]. AIMS Bioengineering, 2022, 9(2): 178-196. doi: 10.3934/bioeng.2022013
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Water-soluble polymers possess great advantages in current drug delivery systems, such as fast delivery through polymer matrix dissolution as well as promoting solid dispersion of poorly water-soluble drugs. In this work, water-soluble polyvinyl alcohol (PVA) and polyethylene oxide (PEO) were blended (50/50) to electrospin with and without the incorporation of a model drug, melatonin (MLT), at various blend polymer concentrations. Results suggested that increasing blend PVA/PEO solution concentrations, up to 7 wt%, promoted the formation of smooth and defect-free drug-incorporating fibers with an average fiber diameter ranged from 300 to 700 nm. Mechanical properties of the blank and MLT-loaded PVA/PEO fibers showed dependence on fiber morphologies and fiber mat structures, due to polymer concentrations for electrospinning. Furthermore, the surface wettability of the blend PVA/PEO fibers were investigated and further correlated with the MLT release profile of the fibers. Results suggested that fiber mats with a more well-defined fiber structure promoted a linear release behavior within 10 minutes in vitro. These drug-incorporated fibers were compatible to human umbilical vein endothelial cells (HUVECs) up to 24 hours. In general, this work demonstrated the structure-property correlations of electrospun PVA/PEO fibers and their potential biomedical applications in fast delivery of small molecule drugs.
Collective behaviors often appear in many classical oscillatory systems [1,4,7,17,18,25,27,29]. Recently, such classical synchronization dynamics has been extended to a quantum regime, and it is called quantum synchronization in literature. It is worthwhile mentioning from [19,20] that quantum synchronization has attracted many researchers in the quantum optics community due to its powerful applications in quantum information and quantum computing [8,14,15,16,21,28,33,34]. Among possible candidates describing quantum synchronization, we are interested in analytical studies on quantum synchronization via Wigner's formalism [30] that was first introduced by Wigner in 1932 in order to find quantum corrections to classical statistical mechanics. For the mathematical properties of the Wigner transform, we refer the reader to [32].
To set up the stage, we begin with the Schördinger-Lohe (SL) model [19]. Let
{i∂tψj=−12Δψj+Vjψj+iκ2NN∑k=1(ψk−⟨ψj,ψk⟩⟨ψj,ψj⟩ψj),t>0,x∈Rd,ψj(0,x)=ψ0j(x),j∈[N]:={1,⋯,N}, | (1) |
where
Note that the Planck constant is assumed to be unity for simplicity. Like the classical Schrödinger equation, system (1) satisfies
In this paper, we study the emergent dynamics of the Cauchy problem to the WL model with identical potentials:
{∂twij+p⋅∇xwij+Θ[V](wij)=κ2NN∑k=1{(wkj+wik)−(∫R2d(wik+wkj)dxdp)wij},t>0,(x,p)∈R2d,wij(0,x,p)=w0ij(x,p),i,j∈[N], | (2) |
subject to initial constraints:
∫R2dw0iidxdp=1,|∫R2dw0ijdxdp−1|<1,i≠j∈[N]. | (3) |
First, we recall the following definition of the emergent dynamics as follows.
Definition 1.1. [3] System (2) exhibits complete aggregation if relative states tend to zero asymptotically.
limt→∞‖wij−wℓm‖L2(R2d)=0,i,j,ℓ,m∈[N]. |
In the sequel, we provide several comments on the Cauchy problem (2)–(3). First, the WL model (2) was first introduced in [3], and a priori asymptotic analysis has been studied only for the two-particle system with
The main results of this paper are two-fold. First, we provide the complete aggregation dynamics of (2) in a priori setting. Under the assumptions (3) on initial data, we can find an invariant set whose center plays the role of an asymptotically stable fixed point (see Lemma 3.2). Then, we obtain the uniform-boundedness of the
Second, we provide a global existence theory of (2) combining the classical methods (fixed point theorem and semigroup theory) and exponential aggregation estimates. We highlight that this paper extends the results in [3] where the existence theory was not considered even for
The rest of this paper is organized as follows. In Section 2, we introduce generalized Wigner functions and the WL distribution matrix, and study their elementary properties. We also review previous results for the WL model. In Section 3, we provide complete aggregation estimates for the WL model in a priori setting. In Section 4, we show the global existence of mild and classical solutions depending on the regularity of initial data. Finally, Section 5 is devoted to a brief summary of this paper and some remaining issues for a future work. In Appendix A, we summarize classical results on the semigroup theory to be used for the global solvability in Section 4.
Gallery of Notation: Throughout the paper, as long as there is no confusion, we simply use
⟨f,g⟩:=∫R2df(x,p)¯g(x,p)dxdp,‖f‖:=√⟨f,f⟩, |
where
(Fϕ)(p):=∫Rdϕ(x)e−ix⋅pdx,(F−1ϕ)(x):=1(2π)d∫Rdϕ(p)eix⋅pdp. |
For a given real-valued function
(Fy→pψ)(x,p):=∫Rdψ(x,y)e−iy⋅pdy. |
In this section, we introduce the
In this subsection, we show how the WL distribution matrix can be constructed from the SL model. For this, we first recall the generalized Wigner distribution and the pseudo-differential operator.
Definition 2.1. [3]
1. For any two complex-valued wave functions
w[ψ,ϕ](x,p):=1(2π)d∫Rdψ(x+y2)¯ϕ(x−y2)eip⋅ydy,(x,p)∈R2d, | (4) |
where
2. For
Θ[V](w)(x,p):=−i(2π)d∫Rd[V(x+y2)−V(x−y2)](Fp′→yw)(x,y)eip⋅ydy=−i(2π)d∫R2d[V(x+y2)−V(x−y2)]w(x,p′)ei(p−p′)⋅ydp′dy. |
Remark 1. Below, we give several comments on the generalized Wigner distribution and the pseudo-differential operator.
1. The generalized Wigner distribution is complex conjugate symmetric in the sense that
w[ϕ,ψ](x,p)=1(2π)d∫Rdϕ(x+y2)¯ψ(x−y2)eip⋅ydy=1(2π)d∫Rd¯ψ(x+y2)ϕ(x−y2)e−ip⋅ydybyy↔−y=¯1(2π)d∫Rdψ(x+y2)¯ϕ(x−y2)eip⋅ydy=¯w[ψ,ϕ](x,p). | (5) |
2. For the case
w[ψ,ψ](x,p)=1(2π)d∫Rdψ(x+y2)¯ψ(x−y2)e−ip⋅ydy. |
Since
w[ψ,ψ]=:w[ψ]. |
Moreover, one can easily verify that
3. The
∫Rdw[ψ](x,p)dp=|ψ(x)|2. |
Moreover, the
∫R2dw[ψ,ϕ](x,p)dxdp=1(2π)d∫R3dϕ(x+y2)¯ψ(x−y2)eip⋅ydydxdp=∫Rdϕ(x)¯ψ(x)dx=⟨ϕ,ψ⟩. |
4. Since
¯Θ[V](w)(x,p)=i(2π)d∫R2d[V(x+y2)−V(x−y2)]ˉw(x,p′)e−i(p−p′)⋅ydp′dy=−i(2π)d∫R2d[V(x−y2)−V(x+y2)]ˉw(x,p′)e−i(p−p′)⋅ydp′dy=−i(2π)d∫R2d[V(x+y2)−V(x−y2)]ˉw(x,p′)ei(p−p′)⋅ydp′dybyy↔−y=Θ[V](¯w)(x,p). |
In the following lemma, we provide several properties of
Lemma 2.2. For
(i)∫R2dΘ[V](f)⋅gdxdp=−∫R2dΘ[V](g)⋅fdxdp.(ii)∫R2dΘ[V](f)dxdp=0. |
Proof. (ⅰ) We use the change of variables:
(p,p′,y)↔(p′,p,−y) |
to yield
∫R2dΘ[V](f)⋅gdxdp=−i(2π)d∫R4d[V(x+y2)−V(x−y2)]f(x,p′)g(x,p)ei(p−p′)⋅ydp′dydxdp=−i(2π)d∫R4d[V(x−y2)−V(x+y2)]f(x,p)g(x,p′)ei(p−p′)⋅ydp′dydxdp=−∫R2dΘ[V](g)⋅fdxdp. |
(ⅱ) By the definition of Definition 2.1 and Fubini's theorem, we have
∫R2dΘ[V](f)dxdp=−i(2π)d∫R4d[V(x+y2)−V(x−y2)]f(x,p′)ei(p−p′)⋅ydp′dydxdp=−i(2π)d∫R3d[V(x+y2)−V(x−y2)]eip⋅y(∫Rdf(x,p′)e−ip′⋅ydp′)dydxdp=−i(2π)d∫R3d[V(x+y2)−V(x−y2)](Fp′→yf)(x,y)eip⋅ydydxdp=−i∫Rd[V(x)−V(x)](Fp′→0f)(x,0)dx=0. |
Remark 2. If we set
∫R2dΘ[V](u)⋅ˉudxdp=−∫R2dΘ[V](ˉu)⋅udxdp=−∫R2d¯Θ[V](u)⋅udxdp=−¯∫R2dΘ[V](u)⋅ˉudxdp. |
This yields
Re[∫R2dΘ[V](u)⋅¯udxdp]=0. |
This fact was used in [23] to show the conservation of
For a given ensemble of wave functions
wij:=w[ψi,ψj],wi:=w[ψ]=w[ψi,ψi],i,j∈[N]. |
Then, the evolution of the WL distributions
∂twij+p⋅∇xwij=−i(2π)d∫R2d[Vi(x+y2)−Vj(x−y2)]wij(x,p′)ei(p−p′)⋅ydp′dy+κ2NN∑k=1[(wkj+wik)−(∫R2dwikdxdp∫R2dwiidxdp+∫R2dwkjdxdp∫R2dwjjdxdp)wij]. | (6) |
For the detailed derivation of (6), we refer the reader to [3]. Next, we show that system (6) admits conservation laws.
Lemma 2.3. Let
Proof. (ⅰ) It follows from (6) that
∂twii+∇x⋅(pwii)+Θ[Vi](wii)=κ2NN∑k=1[(wki+wik)−(∫R2dwikdxdp∫R2dwiidxdp+∫R2dwkidxdp∫R2dwiidxdp)wii]. | (7) |
Now, we integrate (7) over
ddt∫R2dwii(t,x,p)dxdp=0. |
(ⅱ) For the second assertion, we follow a similar calculation in (ⅰ).
Remark 3.
∂tw+p⋅∇xw+Θ[V](w)=0. |
Then by Lemma 2.3, one has
ddt∫R2dw(t,x,p)dxdp=0. | (8) |
However, it is worthwhile mentioning that since
w=w[ψ] |
for a solution
∫R2dw(t,x,p)dxdp=‖ψ(t)‖2L2,t>0. |
Thus, the results in Lemma 2.3 is consistent with the classical theory for the Wigner equation.
‖w(t)‖2=‖ψ(t)‖4. |
Hence, the linear Wigner equation enjoys
From now on, we are concerned with the following special situation:
Vi=Vand∫R2dw0i(x,p)dxdp=1,i∈[N]. | (9) |
In this case, the
∫R2dwi(t,x,p)dxdp=∫R2dw0i(x,p)dxdp=1,t≥0,i∈[N],∫R2dwij(t,x,p,)dxdp=∫R2dw0ij(x,p)dxdp,t≥0,i,j∈[N]. |
Hence, the Cauchy problem for system (6) with (9) can be further simplified as follows:
{∂twij+p⋅∇xwij+Θ[V](wij)=κ2NN∑k=1[(wik+wkj)−(∫R2d(wik+wkj)dxdp)wij],t>0,(x,p)∈R2d,wij(0,x,p)=w0ij(x,p),i,j∈[N]. |
In this subsection, we briefly recall the result from [3] for a two-body system. Extension to the many-body system will be discussed in the following two sections separately. We set
w+12:=Re[w12],z12(t):=∫R2dw12(t,x,p)dxdp,R12(t):=Re[z12(t)]. | (10) |
Then,
{∂tw1+p⋅∇xw1+Θ[V](w1)=κ2(w+12−R12w1),t>0,∂tw2+p⋅∇xw2+Θ[V](w2)=κ2(w+12−R12w2),∂tw12+p⋅∇xw12+Θ[V](w12)=κ4(w1+w2−2z12w12),(w1(0),w2(0),w12(0))=(w01,w02,w012), | (11) |
subject to constraints:
∫R2dw01dxdp=∫R2dw02dxdp=1,|∫R2dw012dxdp|≤1,∫R2dw012dxdp≠−1. | (12) |
Theorem 2.4. [3] Let
|1−z12(t)|≲ |
where
Proof. (ⅰ) The first estimate follows from the following ODE:
This can be integrated explicitly:
(13) |
where
(14) |
then the denominator of the right-hand side of (13) can be zero, and hence
In other words, for initial data satisfying (14),
(ⅱ) It is easy to see that
(15) |
We multiply (15) by
Then, Grönwall's inequality and the first estimate
Before we close this section, we introduce elementary estimates to be used in the following sections.
Lemma 2.5. Let
(16) |
Then, the following assertions hold.
1. If
there exist uniform positive constants
2. If
there exists a uniform constant
Proof. (ⅰ) By the comparison principle of ODE and method of integrating factor, we have
Hence, there exist uniform positive constants
(ⅱ) We multiply (16) with the integrating factor
to find
In this section, we present complete aggregation estimates for (2)–(3) in a priori setting. Our first result can be stated as follows.
Theorem 3.1. Let
(17) |
Proof. Since the proof is rather lengthy, we introduce a strategy toward the proof. We first claim:
For this, the key idea is to derive Grönwall's type differential inequality for
(18) |
Then, we apply Lemma 2.5 to derive the desired zero convergence for
The derivation of (18) will be given in Section 3.2 after some preparatory estimates in Section 3.1.
In this subsection, we study basic estimates for (2)–(3) that will be used in the derivation of (18). We set
Then, it follows from Lemma 2.3 that
(19) |
On the other hand, we integrate (2) with respect to
(20) |
Due to (19), it is natural to consider the maximal diameter for the set
which is expected to converge to zero under a suitable condition.
Lemma 3.2. (Existence of a positively invariant set) Let
(21) |
Then, one has
Proof. It follows from (20) that
(22) |
Then, (22) gives
(23) |
where
By the assumption on initial data, the set
Suppose to the contrary, i.e.,
Then, one has
(24) |
On the other hand, we observe
For
Hence, (23) yields
which contradicts (24). Since
and the set
Remark 4. Lemma 3.2 says that if initial data satisfy (21):
then one has
Thus, the
As a direct consequence of Lemma 3.2, we can also show the uniform
Corollary 1. Let
1. The functional
2. The functional
Proof. (ⅰ) It follows from (20) that
Then, we find a differential inequality for
Lastly, we use initial data (21) together with the above Riccati differential inequality to give the desired result.
(ⅱ) We multiply
(25) |
Now, we integrate (25) with respect to
(26) |
Below, we present estimates for
● Case A.1 (Estimate of
● Case A.2 (Estimate of
● Case A.3 (Estimate of
In (26), we collect all the estimates in Case A.1–Case A.3 to derive
This yields
(27) |
Since
In this subsection, we are ready to provide the proof of Theorem 3.1. First, we claim:
(28) |
Note that if one verifies (28), then (17) follows from the triangle inequality:
We consider the difference between
(29) |
Similar to the proof of Corollary 1, we multiply
(30) |
Below, we present estimates of
● Case B.1 (Estimates of
● Case B.2 (Estimate of
In (30), we combine all the estimates Case B.1–Case B.2 to find
(31) |
If we use Corollary 1 with
(32) |
We sum up (32) with respect to
(33) |
● Case C.1 (Estimate of
(34) |
● Case C.2 (Estimate of
(35) |
In (33), we combine all the estimates (34) and (35) to derive
Finally, we use Lemma 2.5 to establish (28). This completes the proof of Theorem 3.1.
In this section, we show the global existence of a unique mild solution to the Cauchy problem for the WL model (2) following the fixed point approach in [23] where a linear Wigner equation is considered. For this, we define a subset
(36) |
Then, it is easy to check that
For the WL model as a perturbation of the linear Wigner equation, it is strongly believed that
Theorem 4.1. For
1. If initial data and the potential satisfy
then there exists a unique mild solution to the Cauchy problem
2. If we impose further regularity on initial data and the potential
then there exists a unique classical solution to the Cauchy problem
Proof. Since the proof is rather lengthy, we provide the proofs in Section 4.2 and Section 4.3.
In this subsection, we follow the same strategy in [23] in which the linear Wigner equation has been treated by means of the semigroup approach. First, we begin with an elementary property of the transport operator
Lemma 4.2. Let
In other words, the transport operator
Proof. Since a solution
By straightforward calculations, we observe
(37) |
Below, we estimate
● Case C.1 (Estimate of
Hence, we see that
● Case C.2 (Estimate of
By the skew-Hermitian property of
● Case C.3 (Estimate of
In (37), we collect all the estimates in Case C.1–Case C.3 to find
(38) |
We sum up (38) with respect to
It follows from Corollary 1 that
In this subsection, we show that the Cauchy problem for the WL model admits a unique mild solution.
First, we rewrite (2) as a matrix form to apply the fixed point theorem. For
(39) |
where
Then,
equipped with the norm
Now, we are concerned with the global solvability of (39). Let
(40) |
We need to check well-definedness and strict contraction of
● (Well-definedness of
● (Strict contraction): for
If we set
For simplicity, we set
By straightforward calculation,
(41) |
In addition, we observe
(42) |
It follows from Corollary 1 that
Then, (41) and (42) yield
(43) |
and integrate the relation (43) to find
Since
If
Hence,
Next, we are concerned with a global classical solution. In order to apply Theorem A.2(2) in Appendix A for a classical solution to the Cauchy problem (2)–(3), we have to show the continuously differentiability of the coupling term containing
For
which is nonlinear with respect to the argument
Lemma 4.3. For
Then, the functional derivative, denoted by
Proof. For
At each point
Since
Therefore, we verified that
Here,
This shows that
Now, we are ready to provide the second assertion of Theorem 4.1 by applying semigroup theory.
● Step A (the linear Wigner equation on
(44) |
Since (44) on
Since
For details, we refer the reader to [23,Theorem 1].
● Step B (the WL model on
This completes the proof.
In this paper, we have studied the complete aggregation estimate and the global existence of the Wigner-Lohe(WL) model which describes quantum synchronization in the Wigner picture. By taking the Wigner transform on the Schrödinger-Lohe model with identical potentials, we formally derived the WL model which is an integro-differential equation. Compared to the linear Wigner equation, one of the main difficulty to deal with the WL model lies in the lack of conservation laws. However, fortunately, we can overcome the loss of several conserved quantities via collective dynamics. For the WL model, we first establish complete aggregation estimates that can be achieved with an exponential convergence rate in a priori setting. Next, we show that the WL model admits a unique global mild solution by the standard fixed point theorem and if we impose further regularity on initial data, a unique global classical solution can be obtained by using the semigroup theory. Of course, there are still lots of untouched issues. For instance, we focused on the identical WL model where external one-body potentials are assumed to be the same. Thus, the extension of collective dynamics and global solvability of the WL model with non-identical potentials are left for a future work.
In this appendix, we briefly summarize several results in [24] on the semigroup theory to show the existence of evolution equations. The first theorem deals with the bounded perturbation of a linear equation.
Theorem A.1. [24] Let
(i) A is the infinitestimal generator of a
(ii)
Then,
Consider the following abstract Cauchy problem:
(45) |
In next theorem, we recall the result on the mild and classical solutions of (45).
Theorem A.2. [24] The following assertions hold.
1. Let
2. Let
Finally, we recall Gâteaux's mean value theorem. We denote the directional derivative of
Lemma A.3. [2,Proposition A.2] Let
where
[1] |
Szunerits S, Boukherroub R (2018) Heat: A highly efficient skin enhancer for transdermal drug delivery. Front Bioeng Biotechnol 6: 15. https://doi.org/10.3389/fbioe.2018.00015 ![]() |
[2] |
Alshehri S, Imam SS, Hussain A, et al. (2020) Potential of solid dispersions to enhance solubility, bioavailability, and therapeutic efficacy of poorly water-soluble drugs: newer formulation techniques, current marketed scenario and patents. Drug Deliv 27: 1625-1643. https://doi.org/10.1080/10717544.2020.1846638 ![]() |
[3] |
Prajapati SK, Jain A, Jain A, et al. (2019) Biodegradable polymers and constructs: A novel approach in drug delivery. Eur Polym J 120: 109191. https://doi.org/10.1016/j.eurpolymj.2019.08.018 ![]() |
[4] |
Waly AL, Abdelghany AM, Tarabiah AE (2021) Study the structure of selenium modified polyethylene oxide/polyvinyl alcohol (PEO/PVA) polymer blend. J Mater Res Technol 14: 2962-2969. https://doi.org/10.1016/j.jmrt.2021.08.078 ![]() |
[5] |
Bala R, Khanna S, Pawar P (2014) Design optimization and in vitro - in vivo evaluation of orally dissolving strips of clobazam. J Drug Deliv 2014: 1-15. https://doi.org/10.1155/2014/392783 ![]() |
[6] |
Yun YH, Lee BK, Park K (2015) Controlled drug delivery: Historical perspective for the next generation. J Controlled Release 219: 2-7. https://doi.org/10.1016/j.jconrel.2015.10.005 ![]() |
[7] |
Chou S-F, Carson D, Woodrow KA (2015) Current strategies for sustaining drug release from electrospun nanofibers. J Controlled Release 220: 584-591. https://doi.org/10.1016/j.jconrel.2015.09.008 ![]() |
[8] |
Gizaw M, Thompson J, Faglie A, et al. (2018) Electrospun fibers as a dressing material for drug and biological agent delivery in wound healing applications. Bioengineering 5: 9. https://doi.org/10.3390/bioengineering5010009 ![]() |
[9] |
Chou S-F, Woodrow KA (2017) Relationships between mechanical properties and drug release from electrospun fibers of PCL and PLGA blends. J Mech Behav Biomed Mater 65: 724-733. https://doi.org/10.1016/j.jmbbm.2016.09.004 ![]() |
[10] |
Ball C, Chou S-F, Jiang Y, et al. (2016) Coaxially electrospun fiber-based microbicides facilitate broadly tunable release of maraviroc. Mater Sci Eng C 63: 117-124. https://doi.org/10.1016/j.msec.2016.02.018 ![]() |
[11] |
Bagheri M, Validi M, Gholipour A, et al. (2022) Chitosan nanofiber biocomposites for potential wound healing applications: Antioxidant activity with synergic antibacterial effect. Bioeng Transl Med 7: e10254. https://doi.org/10.1002/btm2.10254 ![]() |
[12] |
Moroni I, Garcia-Bennett AE (2021) Effects of absorption kinetics on the catabolism of melatonin released from CAP-coated mesoporous silica drug delivery vehicles. Pharmaceutics 13: 1436. https://doi.org/10.3390/pharmaceutics13091436 ![]() |
[13] |
Al-Zaqri N, Pooventhiran T, Alsalme A, et al. (2020) Structural and physico-chemical evaluation of melatonin and its solution-state excited properties, with emphasis on its binding with novel coronavirus proteins. J Mol Liq 318: 114082. https://doi.org/10.1016/j.molliq.2020.114082 ![]() |
[14] |
Hawkins BC, Burnett E, Chou S-F (2022) Physicomechanical properties and in vitro release behaviors of electrospun ibuprofen-loaded blend PEO/EC fibers. Mater Today Commun 30: 103205. https://doi.org/10.1016/j.mtcomm.2022.103205 ![]() |
[15] | ASTM D1708-18Standard test method for tensile properties of plastics by use of microtensile specimens, West Conshohocken, PA, ASTM International (2018). |
[16] | ASTM D5034-21Standard test method for breaking strength and elongation of textile fabrics (grab test), West Conshohocken, PA, ASTM International (2021). |
[17] |
Hekmati AH, Khenoussi N, Nouali H, et al. (2014) Effect of nanofiber diameter on water absorption properties and pore size of polyamide-6 electrospun nanoweb. Text Res J 84: 2045-2055. https://doi.org/10.1177/0040517514532160 ![]() |
[18] |
Daescu M, Toulbe N, Baibarac M, et al. (2020) Photoluminescence as a complementary tool for UV-VIS spectroscopy to highlight the photodegradation of drugs: A case study on melatonin. Molecules 25: 3820. https://doi.org/10.3390/molecules25173820 ![]() |
[19] |
Haro Durand L, Vargas G, Vera-Mesones R, et al. (2017) In vitro human umbilical vein endothelial cells response to ionic dissolution products from lithium-containing 45S5 bioactive glass. Materials 10: 740. https://doi.org/10.3390/ma10070740 ![]() |
[20] |
Amariei N, Manea LR, Bertea AP, et al. (2017) The influence of polymer solution on the properties of electrospun 3D nanostructures. IOP Conf Ser Mater Sci Eng 209: 012092. https://doi.org/10.1088/1757-899X/209/1/012092 ![]() |
[21] |
Datta R, Yelash L, Schmid F, et al. (2021) Shear-thinning in oligomer melts—Molecular origins and applications. Polymers 13: 2806. https://doi.org/10.3390/polym13162806 ![]() |
[22] |
Mirtič J, Balažic H, Zupančič Š, et al. (2019) Effect of solution composition variables on electrospun alginate nanofibers: Response surface analysis. Polymers 11: 692. https://doi.org/10.3390/polym11040692 ![]() |
[23] |
Briscoe B, Luckham P, Zhu S (2000) The effects of hydrogen bonding upon the viscosity of aqueous poly(vinyl alcohol) solutions. Polymer 41: 3851-3860. https://doi.org/10.1016/S0032-3861(99)00550-9 ![]() |
[24] |
Vlachou M, Siamidi A, Anagnostopoulou D, et al. (2022) Modified release of the pineal hormone melatonin from matrix tablets containing poly(L-lactic acid) and its PLA-co-PEAd and PLA-co-PBAd copolymers. Polymers 14: 1504. https://doi.org/10.3390/polym14081504 ![]() |
[25] |
Angel N, Li S, Yan F, et al. (2022) Recent advances in electrospinning of nanofibers from bio-based carbohydrate polymers and their applications. Trends Food Sci Technol 120: 308-324. https://doi.org/10.1016/j.tifs.2022.01.003 ![]() |
[26] |
Son WK, Youk JH, Lee TS, et al. (2004) The effects of solution properties and polyelectrolyte on electrospinning of ultrafine poly(ethylene oxide) fibers. Polymer 45: 2959-2966. https://doi.org/10.1016/j.polymer.2004.03.006 ![]() |
[27] |
Filip P, Peer P (2019) Characterization of poly(ethylene oxide) nanofibers—Mutual relations between mean diameter of electrospun nanofibers and solution characteristics. Processes 7: 948. https://doi.org/10.3390/pr7120948 ![]() |
[28] |
Ziyadi H, Baghali M, Bagherianfar M, et al. (2021) An investigation of factors affecting the electrospinning of poly (vinyl alcohol)/kefiran composite nanofibers. Adv Compos Hybrid Mater 4: 768-779. https://doi.org/10.1007/s42114-021-00230-3 ![]() |
[29] |
Mwiiri FK, Daniels R (2020) Influence of PVA molecular weight and concentration on electrospinnability of birch bark extract-loaded nanofibrous scaffolds intended for enhanced wound healing. Molecules 25: 4799. https://doi.org/10.3390/molecules25204799 ![]() |
[30] |
Cho D, Netravali AN, Joo YL (2012) Mechanical properties and biodegradability of electrospun soy protein isolate/PVA hybrid nanofibers. Polym Degrad Stab 97: 747-754. https://doi.org/10.1016/j.polymdegradstab.2012.02.007 ![]() |
[31] |
Amjadi M, Fatemi A (2020) Tensile behavior of high-density polyethylene including the effects of processing technique, thickness, temperature, and strain rate. Polymers 12: 1857. https://doi.org/10.3390/polym12091857 ![]() |
[32] | Séguéla R (2007) Plasticity of semi-crystalline polymers: crystal slip versus melting-recrystallization. E-Polym 7: 32. https://doi.org/10.1515/epoly.2007.7.1.382 |
[33] |
Devangamath SS, Lobo B, Masti SP, et al. (2020) Thermal, mechanical, and AC electrical studies of PVA–PEG–Ag2S polymer hybrid material. J Mater Sci Mater Electron 31: 2904-2917. https://doi.org/10.1007/s10854-019-02835-3 ![]() |
[34] |
Rashid TU, Gorga RE, Krause WE (2021) Mechanical properties of electrospun fibers—A critical review. Adv Eng Mater 23: 2100153. https://doi.org/10.1002/adem.202100153 ![]() |
[35] |
Morel A, Domaschke S, Urundolil Kumaran V, et al. (2018) Correlating diameter, mechanical and structural properties of poly(![]() |
[36] | Parab RS, Rao GK (2019) Understanding the mechanical properties of polymer blends in the presence of plasticizers and other additives. Int J Pharm Sci Rev Res 54: 84-91. |
[37] |
Croisier F, Duwez A-S, Jérôme C, et al. (2012) Mechanical testing of electrospun PCL fibers. Acta Biomater 8: 218-224. https://doi.org/10.1016/j.actbio.2011.08.015 ![]() |
[38] |
Ghasemi M, Singapati AY, Tsianou M, et al. (2017) Dissolution of semicrystalline polymer fibers: Numerical modeling and parametric analysis. AIChE J 63: 1368-1383. https://doi.org/10.1002/aic.15615 ![]() |
[39] |
Hirsch E, Pantea E, Vass P, et al. (2021) Probiotic bacteria stabilized in orally dissolving nanofibers prepared by high-speed electrospinning. Food Bioprod Process 128: 84-94. https://doi.org/10.1016/j.fbp.2021.04.016 ![]() |
[40] |
Zhang J, Yan X, Tian Y, et al. (2020) Synthesis of a new water-soluble melatonin derivative with low toxicity and a strong effect on sleep aid. ACS Omega 5: 6494-6499. https://doi.org/10.1021/acsomega.9b04120 ![]() |
[41] |
Khan MQ, Kharaghani D, Nishat N, et al. (2019) Preparation and characterizations of multifunctional PVA/ZnO nanofibers composite membranes for surgical gown application. J Mater Res Technol 8: 1328-1334. https://doi.org/10.1016/j.jmrt.2018.08.013 ![]() |
[42] |
Song X, Gao Z, Ling F, et al. (2012) Controlled release of drug via tuning electrospun polymer carrier. J Polym Sci Part B Polym Phys 50: 221-227. https://doi.org/10.1002/polb.23005 ![]() |
[43] |
Mihailiasa M, Caldera F, Li J, et al. (2016) Preparation of functionalized cotton fabrics by means of melatonin loaded β-cyclodextrin nanosponges. Carbohydr Polym 142: 24-30. https://doi.org/10.1016/j.carbpol.2016.01.024 ![]() |
[44] |
Gulino EF, Citarrella MC, Maio A, et al. (2022) An innovative route to prepare in situ graded crosslinked PVA graphene electrospun mats for drug release. Compos Part Appl Sci Manuf 155: 106827. https://doi.org/10.1016/j.compositesa.2022.106827 ![]() |
[45] |
Torres-Martínez EJ, Vera-Graziano R, Cervantes-Uc JM, et al. (2020) Preparation and characterization of electrospun fibrous scaffolds of either PVA or PVP for fast release of sildenafil citrate. E-Polym 20: 746-758. https://doi.org/10.1515/epoly-2020-0070 ![]() |
[46] |
Carvalho LD de, Peres BU, Maezono H, et al. (2019) Doxycycline release and antibacterial activity from PMMA/PEO electrospun fiber mats. J Appl Oral Sci 27: e20180663. https://doi.org/10.1590/1678-7757-2018-0663 ![]() |
[47] |
Eskitoros-Togay ŞM, Bulbul YE, Tort S, et al. (2019) Fabrication of doxycycline-loaded electrospun PCL/PEO membranes for a potential drug delivery system. Int J Pharm 565: 83-94. https://doi.org/10.1016/j.ijpharm.2019.04.073 ![]() |
[48] |
Yu D-G, Shen X-X, Branford-White C, et al. (2009) Oral fast-dissolving drug delivery membranes prepared from electrospun polyvinylpyrrolidone ultrafine fibers. Nanotechnology 20: 055104. https://doi.org/10.1088/0957-4484/20/5/055104 ![]() |
[49] |
Samprasit W, Akkaramongkolporn P, Ngawhirunpat T, et al. (2015) Fast releasing oral electrospun PVP/CD nanofiber mats of taste-masked meloxicam. Int J Pharm 487: 213-222. https://doi.org/10.1016/j.ijpharm.2015.04.044 ![]() |
[50] |
Huang C-Y, Hu K-H, Wei Z-H (2016) Comparison of cell behavior on pva/pva-gelatin electrospun nanofibers with random and aligned configuration. Sci Rep 6: 37960. https://doi.org/10.1038/srep37960 ![]() |
[51] |
Yang JM, Yang JH, Tsou SC, et al. (2016) Cell proliferation on PVA/sodium alginate and PVA/poly(γ-glutamic acid) electrospun fiber. Mater Sci Eng C 66: 170-177. https://doi.org/10.1016/j.msec.2016.04.068 ![]() |
[52] |
Carrasco-Torres G, Valdés-Madrigal M, Vásquez-Garzón V, et al. (2019) Effect of silk fibroin on cell viability in electrospun scaffolds of polyethylene oxide. Polymers 11: 451. https://doi.org/10.3390/polym11030451 ![]() |
[53] |
Cerqueira A, Romero-Gavilán F, Araújo-Gomes N, et al. (2020) A possible use of melatonin in the dental field: Protein adsorption and in vitro cell response on coated titanium. Mater Sci Eng C 116: 111262. https://doi.org/10.1016/j.msec.2020.111262 ![]() |
[54] | Cheng J, Yang H, Gu C, et al. (2018) Melatonin restricts the viability and angiogenesis of vascular endothelial cells by suppressing HIF-1α/ROS/VEGF. Int J Mol Med 43: 945-955. https://doi.org/10.3892/ijmm.2018.4021 |
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